Jason Pierre-Paul said he wants to come back to the Giants, but only on his terms.

That means no more short-term contracts and he added adamantly that he was not interested in the franchise tag.

“I’m not signing another one-year deal,” Pierre-Paul said at the Giants practice facility, a day after the team’s season ended with a 38-13 wild-card playoff loss in Green Bay.

“I’ve proved it, I’ve showed it,” said Pierre-Paul, who missed Sunday’s playoff game following his December surgery for a sports hernia. “There’s not another guy like me doing it with 7 ¹/₂ fingers.”

Asked about his desire for a multi-year deal, general manager Jerry Reese said, “Players should say that.”

Pierre-Paul’s infamous fireworks accident cost him part of his right hand in 2015, and after playing the final eight games of last season, Pierre-Paul signed a one-year, $10 million contract for 2016.

And he played well, with seven sacks and three forced fumbles in 12 games — before suffering the sports hernia last month. He had 5 ½ sacks in his final two game prior to the injury.

The 28-year-old said he would have been able to return to the lineup next weekend, had the Giants advanced to face the Cowboys.

He insisted the injury is not a concern.

“The reality is I proved myself,” Pierre-Paul said. “I’ll come back from this fine.”

The Giants made a significant investment in their defensive line last offseason, bringing in Olivier Vernon and Damon Harrison. They will have to decide whether they are willing to add another large multi-year contract at the position.

Not surprisingly, coach Ben McAdoo said he hopes Pierre-Paul sticks around East Rutherford.

“Do I want him back? JPP is a heck of a player,” the McAdoo said. “He makes a lot of things easier on defense. Sure [I want him back].”

Reese agreed.

“We are in the genesis of the offseason evaluation and we keep all of our options open, and we will try to do what is best for everybody involved in the situation,’’ Reese said. “Do we want him back? Of course we want him back. He’s a good football player. We’ll see how everybody fits into the puzzle. As many good players you can have, you want them on your roster and Jason’s a good player.”

And he said it could be possible to bring back both Pierre-Paul and Johnathan Hankins.

But there’s the reality of the salary cap to wrestle with.

“You can’t keep everybody,” Vernon said. “That’s the nature of the beast. … If JPP is back, that would be great, but he has to [make] the best decision he can for himself. We’ll see how that goes.”

Harrison said: “Hopefully we see him back next year.”

For Pierre-Paul’s part, the defensive end said he would “love to return” to the Giants, especially because of his new teammates on the defensive line, but stressed it would be a “business decision.”

“Those guys got what they deserved,” Pierre-Paul said of last year’s free-agent class. “I have a family. We’ll sit down and talk about the process. This is a business. I don’t work for free.”